Asymptotic metric behavior of random Cayley graphs of finite abelian groups

TL;DR

This paper establishes limit laws for metric parameters of random Cayley graphs of finite abelian groups, confirming a conjecture and advancing understanding of their asymptotic behavior.

Contribution

It introduces new limit laws for metric parameters of random Cayley graphs of finite abelian groups, settling a previously conjectured behavior.

Findings

Established several limit laws for metric parameters

Confirmed a conjecture of Amir and Gurel-Gurevich

Applied methods of Marklof and Strömbergsson

Abstract

Using methods of Marklof and Str\"ombergsson we establish several limit laws for metric parameters of random Cayley graphs of finite abelian groups with respect to a randomly chosen set of generators of a fixed size. Doing so we settle a conjecture of Amir and Gurel-Gurevich.